of 6
Supplementary Information for
Position-specific and Clumped Stable Isotope Studies: Comparison of the
Urey and Path-Integral Approaches for Carbon Dioxide, Nitrous Oxide,
Methane, and Propane
Michael A. Webb and Thomas F. Miller III
Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
E-mail: tfm@caltech.edu
Contents
PIMC Partition function ratios and equilibrium constants . . . . . . . . . . . . . . . . . S-2
Normal mode wave numbers for CO
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . S-3
Normal mode wave numbers for N
2
O . . . . . . . . . . . . . . . . . . . . . . . . . . . S-4
Normal mode wave numbers for methane. . . . . . . . . . . . . . . . . . . . . . . . . . S-5
Zero-point energies for Urey-AHO calculations . . . . . . . . . . . . . . . . . . . . . . S-6
*
To whom correspondence should be addressed
S-1
Table S - 1:
Partition function ratios and equilibrium constants calculated using PIMC. Statistical errors
are in parentheses and apply to the last digit.
T (K)
16
O
13
C
18
O
-HB
16
O
13
C
18
O
-LB
R
16
O
12
13
C
16
O
R
16
O
12
13
C
18
O
K
R
16
O
12
13
C
16
O
R
16
O
12
13
C
18
O
K
300
1
.
34246
(
8
)
1
.
34374
(
7
)
0
.
99904
(
8
)
1
.
340520
(
9
)
1
.
341808
(
9
)
0
.
999040
(
9
)
400
1
.
26788
(
3
)
1
.
26861
(
5
)
0
.
99942
(
5
)
1
.
26634
(
1
)
1
.
267067
(
9
)
0
.
99943
(
1
)
500
1
.
22730
(
2
)
1
.
22774
(
5
)
0
.
99964
(
4
)
1
.
225898
(
6
)
1
.
226335
(
6
)
0
.
999643
(
7
)
600
1
.
20224
(
6
)
1
.
20254
(
3
)
0
.
99975
(
6
)
1
.
201292
(
4
)
1
.
201571
(
3
)
0
.
999768
(
5
)
T (K)
14
N
15
N
16
O
13
CH
3
D
R
14
15
N
14
N
16
O
R
14
N
14
15
N
16
O
K
R
12
13
CH
4
R
12
13
CH
3
D
K
300
1
.
25485
(
7
)
1
.
19879
(
8
)
0
.
95533
(
8
)
1
.
25495
(
4
)
1
.
26215
(
5
)
0
.
99429
(
5
)
400
1
.
20456
(
5
)
1
.
16818
(
8
)
0
.
96980
(
8
)
1
.
21374
(
4
)
1
.
21799
(
3
)
0
.
99651
(
4
)
500
1
.
17666
(
6
)
1
.
15091
(
7
)
0
.
97812
(
7
)
1
.
19024
(
1
)
1
.
19297
(
4
)
0
.
99771
(
3
)
600
1
.
15954
(
7
)
1
.
14014
(
7
)
0
.
98327
(
7
)
1
.
17547
(
4
)
1
.
17725
(
3
)
0
.
99849
(
4
)
T (K)
12
CH
3
12
CHD
12
CH
3
12
CH
3
13
CH
2
12
CH
3
R
1
2
H
t
R
1
2
H
c
K
R
1
2
C
t
R
1
2
C
c
K
300
32
.
412
(
8
)
29
.
505
(
9
)
0
.
9103
(
4
)
1
.
29398
(
3
)
1
.
27525
(
5
)
0
.
98553
(
4
)
400
14
.
647
(
3
)
13
.
887
(
4
)
0
.
9481
(
3
)
1
.
23400
(
3
)
1
.
22403
(
2
)
0
.
99192
(
3
)
500
9
.
282
(
2
)
8
.
975
(
2
)
0
.
9669
(
2
)
1
.
20158
(
3
)
1
.
19602
(
3
)
0
.
99538
(
3
)
600
6
.
946
(
1
)
6
.
794
(
1
)
0
.
9781
(
2
)
1
.
18212
(
1
)
1
.
17877
(
2
)
0
.
99716
(
2
)
S-2
Table S - 2:
Calculated normal mode wave numbers for CO
2
isotopologues
̄
ω
(cm
1
)
16
O
12
C
16
O
16
O
13
C
16
O
16
O
12
C
18
O
16
O
13
C
18
O
̄
̄
ω
1
672
.
8652
653
.
7147
667
.
7360
648
.
4339
̄
ω
2
672
.
8652
653
.
7147
667
.
7360
648
.
4339
̄
ω
3
1353
.
6090
1353
.
6090
1314
.
5261
1314
.
4491
̄
ω
4
2396
.
2675
2328
.
0668
2378
.
4771
2309
.
7949
Calculated from potential energy surface given by Zúñiga et al.,
J. Mol. Spectrosc.
1999
,
195
, 137–146
S-3
Table S - 3:
Calculated normal mode wave numbers for N
2
O isotopologues.
̄
ω
(cm
1
)
14
N
14
N
16
O
14
N
15
N
16
O
15
N
14
N
16
O
̄
ω
1
596
.
3070
582
.
6763
592
.
7572
̄
ω
2
596
.
3070
582
.
6763
592
.
7572
̄
ω
3
1298
.
2802
1296
.
4726
1281
.
2784
̄
ω
4
2282
.
1801
2232
.
9808
2259
.
4610
Calculated from potential energy surface given by Zúñiga et al.,
J. Chem. Phys.
1999
,
110
, 6339–6352
S-4
Table S - 4:
Calculated normal mode wave numbers for methane isotopologues.
̄
ω
(cm
1
)
12
CH
4
13
CH
4
12
CH
3
D
13
CH
3
D
̄
ω
1
1345
.
3267
1336
.
9620
1188
.
0862
1179
.
9753
̄
ω
2
1345
.
3267
1336
.
9620
1188
.
0862
1179
.
9753
̄
ω
3
1345
.
3267
1336
.
9620
1339
.
8201
1332
.
5799
̄
ω
4
1570
.
3634
1570
.
3634
1508
.
0909
1507
.
0911
̄
ω
5
1570
.
3634
1570
.
3634
1508
.
0909
1507
.
0911
̄
ω
6
3036
.
1496
3036
.
1496
2285
.
1892
2273
.
9839
̄
ω
7
3157
.
0668
3145
.
8475
3071
.
4074
3067
.
7074
̄
ω
8
3157
.
0668
3145
.
8475
3156
.
7900
3145
.
5356
̄
ω
9
3157
.
0668
3145
.
8475
3156
.
7900
3145
.
5356
Calculated from potential energy surface given by Lee et al.,
J. Chem. Phys.
1995
,
102
,
254–261
S-5
Table S - 5:
Zero-point energies (cm
1
) for Urey-AHO calculations.
16
O
13
C
18
O
14
N
15
N
16
O
13
CH
3
D
Isotopologue
E
0
Isotopologue
E
0
Isotopologue
E
0
16
O
12
C
16
O
2525
.
394
14
N
14
N
16
O
2370
.
470
12
CH
4
9638
.
564
16
O
13
C
16
O
2472
.
905
14
N
15
N
16
O
2331
.
890
13
CH
4
9610
.
417
16
O
12
C
18
O
2492
.
277
15
N
14
N
16
O
2347
.
310
12
CH
3
D
9032
.
497
16
O
13
C
18
O
2439
.
355
13
CH
3
D
9002
.
365
S-6